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We study a class of charged cosmological black holes defined by theShah-Vaidya solution, which is similar to the McVittie solution but for acentral object of nonzero electric charge. We show that the Shah-Vaidya metricis a solution of Einstein's equations with a cuscuton and a Maxwell fields assources, as well as a mass parameter. We then analyze the possible causalstructures of the solution under some few physically reasonable assumptions,and determine the regions in the parameter space corresponding to well behavedcharged cosmological black holes and those corresponding to nakedsingularities. The asymptotic behavior of the Hubble factor $H(t)$ is alsodeterminant to the causal properties of the spacetime and a theorem explainingits effect is stated. Examples of causal diagrams covering all the possiblestypes of spacetimes allowed by our initial assumptions are drawn and discussed.

Charged cosmological black holes: a thorough study of a family of solutions